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In fixed beam the slope at the supports be____________
Minimum
Zero
Maximum
Throughout
Zero
In a fixed (or encastr├й) beam, both ends are rigidly built-in or restrained against rotation and translation. Due to this rigid connection, the tangent to the elastic curve at the supports remains horizontal, meaning the slope (╬╕) is zero at both supports.
In a fixed (or encastr├й) beam, both ends are rigidly built-in or restrained against rotation and translation. Due to this rigid connection, the tangent to the elastic curve at the supports remains horizontal, meaning the slope (╬╕) is zero at both supports.
╬╕AтАЛ=0 тАФ Slope at left fixed support
╬╕BтАЛ=0 тАФ Slope at right fixed support
╬┤AтАЛ=0,╬┤BтАЛ=0 тАФ Deflection at fixed supports
The fixed support provides a reactive moment (MfтАЛ) capable of counteracting the rotation that would otherwise be caused by applied loads. By enforcing the boundary condition ╬╕=0 at the supports, the beam's elastic curve is forced to maintain the original orientation of the neutral axis at the fixed end.
Fixed beams are statically indeterminate structures of the third degree.
The reaction at fixed supports includes both a vertical force and a restraining moment.
The slope is the first derivative of the deflection equation (yтА▓).
Reduced maximum bending moment compared to simply supported beams.
Higher stiffness and lower deflection under identical loading.
Sensitive to support settlement and temperature changes.
Requires precise construction for perfect end rigidity.
Continuous bridge decks.
Rigid frame building structures.
In a simply supported beam, the slope is maximum at the supports.
Option B is the correct choice because the definition of a fixed end is that it permits no rotation (slope = 0).
B is correct тАФ By definition, a fixed support restricts rotation, resulting in zero slope at the support points.
Always remember that for fixed beams, the number of redundant reactions (two moments and two vertical reactions minus equilibrium equations) is two; hence, they are highly sensitive to support alignment.
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